Skip to main content
SpringerLink
Log in

Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions

  • Conference paper
  • First Online:
Complex Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 599))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17 (1915), 12–22.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Biernacki, Sur la représentation conforme des domaines linéairement accessible, Prace Frat. Fiz. 44 (1937), 293–314.

    MATH  Google Scholar 

  3. S. Bochner and W. T. Martin, Several Complex Variables, Princeton University Press, 1948.

    Google Scholar 

  4. K. R. Gurganus, Φ-like holomorphic functions in C n and Banach spaces, Trans. Amer. Math. Soc. 205 (1975), 389–406.

    MathSciNet  MATH  Google Scholar 

  5. L. A. Harris, Schwarz's Lemma in normed linear spaces, Proc. Natl. Acad. Sci. U.S.A. 64(4), (1969), 1014–1017.

    Article  MATH  Google Scholar 

  6. E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ. 31 (1957).

    Google Scholar 

  7. W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Lewandowski, Sur l'identité de certaines classes de fonctions univalentes, I and II, Ann. Univ. Mariae Curie-Sklodowska, Sect. A, 12 (1958), 131–146 and 14 (1960), 19–46.

    MathSciNet  Google Scholar 

  9. T. Matsuno, Starlike theorems and convex-like theorems in the complex vector space, Sci. Rep. Toko, Kyoiku Daigaku, Sect. A, 5 (1955), 88–95.

    MathSciNet  MATH  Google Scholar 

  10. J. A. Pfaltzgraff, Subordination chains and univalence of holomorphic mappings on C n, Math. Ann. 210 (1974), 55–68.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. A. Pfaltzgraff and T. J. Suffridge, Close-to-starlike holomorphic functions of several variables, Pac. J. Math. 57 (1975), 271–279.

    Article  MathSciNet  MATH  Google Scholar 

  12. Ch. Pommerenke, Über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159–173.

    MathSciNet  MATH  Google Scholar 

  13. M. S. Robertson, Applications of the subordination principle to univalent functions, Pac. J. Math. 11 (1961), 315–324.

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Spaček, Contibution à la theorie des fonctions univalentes, Časopsis Pěct. Mat. 62 (1932), 12–19.

    MATH  Google Scholar 

  15. T. J. Suffridge, The principle of subordination applied to functions of several variables, Pac. J. Math. 33 (1970), 241–248.

    Article  MathSciNet  MATH  Google Scholar 

  16. —, Starlike and convex maps in Banach spaces, Pac. J. Math. 46 (1973), 575–589.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Kentucky, 40506, Lexington, Kentucky

    T. J. Suffridge

Authors
  1. T. J. Suffridge
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

James D. Buckholtz Teddy J. Suffridge

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Suffridge, T.J. (1977). Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions. In: Buckholtz, J.D., Suffridge, T.J. (eds) Complex Analysis. Lecture Notes in Mathematics, vol 599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096834

Download citation

  • DOI: https://doi.org/10.1007/BFb0096834

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08343-6

  • Online ISBN: 978-3-540-37303-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation